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In mathematics, an exceptional Lie algebra is a complex simple Lie algebra whose Dynkin diagram is of exceptional type. There are exactly five of them: g 2 , f 4 , e 6 , e 7 , e 8 {\displaystyle {\mathfrak {g}}_{2},{\mathfrak {f}}_{4},{\mathfrak {e}}_{6},{\mathfrak {e}}_{7},{\mathfrak {e}}_{8}} ; their respective dimensions are 14, 52, 78, 133, 248. The corresponding diagrams are:
In contrast, simple Lie algebras that are not exceptional are called classical Lie algebras.